joseph f. johnson

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bio	website	www34.homepage.villanova.edu/…
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Haverford (mental institution) MIT (yet another) Tufts, Univ. of Utah (in East Berlin), Rutgers (near East Berlin, NJ), Villanova, Notre Dame, Univ. of New Hampshire, Hostos-CUNY, Queen's Univ. (Canadá).

	1,928 reputation	bio	website	www34.homepage.villanova.edu/…	visits	member for	1 year, 5 months
212 badges		location	Centro Habana		seen	Mar 3 at 5:53

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Feb 21	comment	Prerequisites to start the study of noncommutative geometry in physics During Hilbert's lifetime, Hecke (his student) was way under-appreciated. The big man was Landau. Nowadays, where is Landau? But Hecke's work is seen as more and more important every day.... I predict the same for Vergne.
Feb 20	awarded	Revival
Feb 16	comment	Ignorance in statistical mechanics You are welcome to introduce your own interpretation, but it is difficult to make out a case that Landau and Dirac had the same interpretation as you. Landau was notoriously woolly on foundational questions, and Dirac never addressed the philosophical issues about probability that you (and me, too) are interested in, when you (correctly) point out «the old ignorance interpretation generates many problems and paradoxes » but Dirac did not care about them a bit. Some of the people who do have postulated Density matrices as a new foundation for QM to try to get out of the paradoxes that way.
Feb 16	comment	Ignorance in statistical mechanics Now look up Gibbs density in Dirac's The Principles of Quantum Mechanics, and you'll see he explicitly says it is analogous to Classical Statistical Mechanics: «We shall now see that there exists a corresponding density $p$ in quantum mechanics, having properties analogous to the above. It was first introduced by von Neumann. Its existence is rather surprising...» and later, «Let us now suppose that initially the System, instead of being certainly in the state CX', is in one or other of various states 01' with the probability Pa, for each.» He is using the classical notion of probability
Feb 16	comment	Ignorance in statistical mechanics See physics.stackexchange.com/a/53629/6432 and my comment on it. Landau says «The averaging by means of the statistical matrix ... has a twofold nature. It comprises both the averaging due to the probabilistic nature of the quantum description (even when as complete as possible) and the statistical averaging necessitated by the incompleteness of our information concerning the object considered...It must be borne in mind, however, that these constituents cannot be separated...» I.e., Landau explicitly says the use of the density matrix is due to the incompleteness of our knowledge.
Feb 14	revised	Why do we consider the evolution (usually in time) of a wave function? found Dirac's exact words....
Feb 14	revised	Why do we consider the evolution (usually in time) of a wave function? Add remarks apropos the more general question of the O.P.
Feb 14	answered	Why do we consider the evolution (usually in time) of a wave function?
Feb 14	comment	How to interpret the derivative in the momentum operator in quantum mechanics? A good answer but the phrase «there is absolutely nothing noncommutative in the integrals you write down» is not completely correct and could be a little misleading, since it contradicts the trenchant comment by @QMechanic . Look at the integrand in the right hand side of the first equality, basically $\psi ^D \psi$. Now the Laplacian does not commute with functions...this isnt the same as $D \psi^\psi$, and note, it isn't associative either. I know that to contradict this is not what you meant, but it's what you said, so some editing is in order. (Editing and posting aren't commutative..
Feb 14	comment	Is there a recognised standard for typesetting quantum mechanical operators? Roman letters are not used for functions if the name of the function is a single letter. Even if it comes from a word or name like «Hamilton» or «derivative».
Feb 14	answered	Is there a recognised standard for typesetting quantum mechanical operators?
Feb 14	comment	Why quantum mechanics? I think you have misunderstood the whole point of what the O.P. was asking for, although your contribution might have been valuable as an answer to a different question. What your answer lacks is any compelling immanent critique of Classical Mechanics, an explanation of why it cannot possibly be true. And it wasn't experiments that suggested the Heisenberg uncertainty relations since the experiments then weren't good enough to get anywhere near the theoretical limits. Only recently have such fine measurements been attained.
Feb 14	revised	What is a tensor? grammar fixed in two places
Feb 14	suggested	suggested edit on What is a tensor?
Feb 14	answered	Why is the covariant derivative of the metric tensor zero?
Feb 12	answered	What is the significance of negative frequency in Fourier transform?
Feb 12	comment	Magnitude of the Fourier Transform of White Noise presumably the OP will use the same conventions for each signal, so the analytical relationship does not depend on the conventions used. Hopefully, the same sampling rate and time interval for sampling will be used each time, too.
Feb 12	answered	Magnitude of the Fourier Transform of White Noise
Feb 12	comment	Magnitude of the Fourier Transform of White Noise I assume you mean power spectrum, not Fourier transform, since that's what most instruments measure, and it's what your graph looks like. The power spectrum is usually defined not as the proportion of power, but as the amount of power, so there will be a difference.
Feb 12	comment	Ignorance in statistical mechanics Landau never expresses himself clearly on foundational matters, the way von Neumann always did. Yet Landau was incomparably the greater physicist, I would in fact deny that von Neumann was a physicist at all, not even a mathematical physicist. He was superb at foundational considerations in maths, and logic, but had no physical intuition at all. You are also wrong about Dirac: Dirac had not the slightest intention to make the density matrix a description of the quantum state of a system. It was, for him, a description of the mixed quantum state in analogy to classical mixed state.